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emerson heath - an introduction to c*-algebras and noncommutative geometry

An Introduction to C*-Algebras and Noncommutative Geometry




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Dettagli

Genere:Libro
Lingua: Inglese
Editore:

Birkhäuser

Pubblicazione: 07/2024
Edizione: 2024





Trama

This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover, it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse at some of the more advanced topics of the subject.  Coverage includes C*-algebra theory, K-theory, K-homology, Index theory and Connes’ Noncommuntative Riemannian geometry. 

Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their understanding of noncommutative geometry  and algebraic K-theory. A wide range of important examples are introduced at the beginning of the book. There are lots of excellent exercises and any student working through these will benefit significantly. Prerequisites include  a basic knowledge of algebra, analysis, and a bit of functional analysis.  As the book progresses, a little more mathematical maturity is required as the text discusses smooth manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained though occasionally the reader may opt to consult more specialized material to further deepen their understanding of certain details.





Sommario

An introduction to C*-algebras.- An Introduction to Index Theory and Noncommutative Geometry.- Spectral Theory and Representation.- Positivity, Representations, Tensor Products and Ideals in C*-algebras.- Module theory of C*-algebras.- Morita Equivalence.- Topological K-theory and Clifford Algebras.- K-theory for C*algebras.- The Index Theorem of Atiyah and Singer.- K-homology and Noncommutative Geometry.- An Introduction to KK-theory.- Bibliography.





Autore

Heath Emerson is Professor of Mathematics at the University of Victoria, British Columbia. His research interests include noncommutative geometry, equivariant K-theory, and the Baum–Connes conjecture.











Altre Informazioni

ISBN:

9783031598494

Condizione: Nuovo
Collana: Birkhäuser Advanced Texts Basler Lehrbücher
Dimensioni: 235 x 155 mm
Formato: Copertina rigida
Illustration Notes:XIII, 539 p. 27 illus.
Pagine Arabe: 539
Pagine Romane: xiii


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